Two stroke engines normally smoke heavy when first started and more so after setting for an extended period - you will need to run it for a quarter to half an hour to determine anything. The type of two stroke oil and method of mixing will have an effect on how much it smokes too. Synthetic oils smoke less, but drip from the exhaust. Mineral oils smoke more, create carbon build-up in the exhaust, but drip out of the exhaust less or not at all. If premixing the oil, the type of oil and the type of fuel both play a part in the amount of smoke. Most oils will not mix with alcohol, so during premixing, the oil may force the alcohol to separate from the gasoline and the oil may not mix properly with the gas causing smoking, hard starting, low power and oil dripping from the exhaust.
That splooge inside the recoil cover is a mix of oil and water. It's not uncommon for a two stroke to push some oil past the crank seal behind the flywheel. The recoil cover will get water in it from the outside by migration through the recoil rope hole. That's why the recoil handle fits over the nipple on the cover and has a wire ring on it to seal out water when riding or washing. The cover can also get water in it from condensation. Over a long storage period, condensation will occur and collect. It's one of the reasons there is a drain plug on the bottom of the recoil chamber. It's supposed to drained periodically especially after a day of water crossings.
A table spoon of water from condensation and a tablespoon of oil from engine operation could result in the gooey mess you found when you removed the cover. Clean it, install the cover and run it for awhile checking the counterbalance oil each day. If the counterbalance oil level stays up and coolant is not being lost, just run it and enjoy. The smoke will decrease with run time and engine heat.